Nickel, cobalt, and magnesium often coexist in the sulphate leach liquor of laterite nickel ores, and magnesium will affect the following refining process of nickel and cobalt. In this paper, magnesium oxide slurry was employed to precipitate and separate nickel and cobalt from magnesium with the precipitation method. The appropriate conditions to maximize the precipitation of nickel and cobalt and minimize the precipitation of magnesium are investigated systematically as follows: magnesium oxide addition (nMgO: (nNi + nCo)) = 2.0, hydrolysis time ≤ 2 h, hydrolysis temperature ≥ 60 °C, and stirring speed ≤ 350 rpm. The equilibrium pH, which can be controlled by adjusting the amount of magnesium oxide and temperature, was found to be the main influence factor, and the optimal equilibrium pH of the sulphate leach liquor should be controlled at 8.98. The high precipitations of 98.1% for nickel and 99.1% for cobalt can be obtained with low precipitation of 0.2% for magnesium. The characterizations of the mixed precipitate by XRD, FTIR, and TG–DTG demonstrate the presence of Ni2(CO3)(OH)2 and NiSO4·2H2O except for the primary Ni(OH)2 and Co(OH)2. The nickel and cobalt in the precipitate can be easily transferred into the low acidic solution by leaching at ambient temperature. The regenerated magnesium oxide powder with a high purity can be obtained by calcining the precipitates, which can be recycled as the precipitating agent again.